Penalized variable selection methods and various penalty functions have been widely investigated under different models. Some of the popular penalties proposed in the literature include least absolute shrinkage and selection operator (LASSO) proposed by [1]} for linear models. [2]} proposed Adaptive LASSO to improve the performance of LASSO by incorporating some adaptive weights to achieve oracle properties. A non-convex penalty, smoothly-clipped absolute deviation (SCAD), was proposed by [3]} for linear models. [4]} used SCAD under the Cox regression model. Among the existing penalties, it is well-known that \(L_0\)  penalization enjoys the most excellent optimal properties for estimation and variable selection as it directly penalizes the cardinality of the model [5]}. However, working with this penalty in high-dimensional data is not feasible. Variable selection, in that case, would be an NP-hard problem, and searching for the best subset with a non-convex penalty function makes it impractical to select essential variables.
